Advertisements
Advertisements
Question
A milk container of height 16 cm is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.
Advertisements
Solution
Given that, height of milk container (h) = 16 cm,
Radius of lower end of milk container (r) = 8 cm
And radius of upper end of milk container (R) = 20 cm
∴ Volume of the milk container made of metal sheet in the form of a frustum of a cone
= `(πh)/3 (R^2 + r^2 + Rr)`
= `22/7 xx 16/3 [(20)^2 + (8)^2 + 20 xx 8]`
= `(22 xx 16)/21 (400 + 64 + 160)`
= `(22 xx 16 xx 624)/21`
= `219648/21`
= 10459.42 cm3 ......[∵ 1L = 1000 cm3]
= 10.45942 L
So, volume of the milk container is 10459.42 cm3
∵ Cost of 1 L milk = ₹ 22
∴ Cost of 10.45942 L milk = 22 × 10.45942 = ₹ 230.12
Hence, the required cost of milk is ₹ 230.12
APPEARS IN
RELATED QUESTIONS
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8 per 100 cm2. [Take π = 3.14]
A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained is drawn into a wire of diameter 1/16 cm, find the length of the wire [use π=22/7]
The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity.( \[\pi = \frac{22}{7}\])
A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many litres of milk it contains if it is full to the brim? If the milk is sold at Rs 40 per litre, find the amount received by the person.
A circus tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.
A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the cone and of the remaining solid left out after the cone carved out.
An icecream cone full of icecream having radius 5 cm and height 10 cm as shown in fig. 16.77. Calculate the volume of icecream , provided that its 1/ 6 part is left unfilled with icecream .
The radii of the base of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?
If r1 and r2 denote the radii of the circular bases of the frustum of a cone such that r1 > r2, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is
A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.
A bucket is in the form of a frustum of a cone. Its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm, respectively. Find how many litres of water can the bucket hold.
The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area. [Use π = 3.14.]
A milk container is made of metal sheet in the shape of frustum of a cone whose volume is `"10459" 3/7 "cm"`. The radii of its lower and upper circular ends are 8 cm and 20 cm, respectively. Find the cost of metal sheet used in making the container at the rate of ₹1.40 per cm2.
A funnel is a combination of
A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left is called
A frustum of a right circular cone is of height 16 cm with radius of its ends as 8 cm and 20 cm. Then, the volume of the frustum is
The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is ______.
The volume of the frustum of a cone is `1/3 pih[r_1^2 + r_2^2 - r_1r_2]`, where h is vertical height of the frustum and r1, r2 are the radii of the ends.
If radius of the base of cone is 7 cm and height is 24 cm, then find its slant height.
